'Where's the beef?" asked one headline after the prime minister's speech at the Lord Mayor's Banquet on Monday. The complaint, repeated in a number of places, is that his first major intervention on foreign affairs served up some interesting hors d'oeuvres but failed to provide a satisfying main course. In particular, he didn't set out an overarching vision that might make sense of some worthwhile policy detail. This is a criticism that has already become familiar on the domestic front.

It is true that "hard-headed internationalism" is unlikely to become known as the "Brown doctrine" and studied in years to come. Almost every government aspires to reconcile the advancement of national interest with the noble ambition of making the world a better place. But there were more interesting passages in his speech that failed to get the attention they merited and would, if followed with Gordon Brown's usual intellectual rigour, lead to some very radical conclusions.

The most important of these is the vision of an emerging "global society" that recurred throughout his speech. This appears to be more than a throwaway line or a synonym for the more commonplace idea of international community. The latter has come to refer exclusively to relations between states within established international structures like the UN. Brown's idea is rooted in the experience of globalisation and the knowledge that the opportunities offered by rising personal mobility and the communications revolution are increasingly bringing populations into direct contact, creating new networks and relationships beyond traditional state-to-state diplomacy. Brown didn't quite say so, but what he described is the emergence of a global citizenry.

This has transformative implications for the existing model of international relations and particularly the primacy of state sovereignty on which it is based. If people are in the process of forming a global society, is it not time that the doctrine of popular sovereignty gained its rightful place as the foundation stone of a new global order? Isn't it time for the laws and institutions of the international system to reflect the rights of the individuals who live under them, and to do so in a much more direct way? After all, that's what happens in any recognisable democratic society.

One major objection might be that popular sovereignty has no way of finding a voice in countries that are not democracies, not least China. That is true, so the only way forward is to dispense, at least informally, with the principle of sovereign equality between states. It is nonsense to give equal weight to the opinions of states that respect the will of their citizens and those that reflect only the interests of their unelected rulers.

This is not an argument for throwing China off the UN security council, but for asserting the moral superiority of democratic governance and developing alliances that give expression to it. The prime minister may have had something like this in mind when he called for "a new coalition of democracies and civic societies, joining together as allies for progress". The potential is certainly there now that almost two-thirds of countries in the world are recognised electoral democracies. Because of this it is entirely possible that instead of another bipolar standoff between democratic and authoritarian superpowers, the coming world order will have several poles, most of which are democratic. It should be an objective of British policy to make sure that it does.

Progressives, suspicious that this might be the smokescreen for a new neoconservative agenda, shouldn't worry. The idea of a democratic multipolar world is as unappealing to the Project for the New American Century as it is to the central committee of the Chinese Communist party. American unipolarists don't want to share power with anyone else, whether they are democracies or not. It would constrain them too much and make future follies on the scale of Iraq impossible. This is where Brown will need to embrace a third heresy: a close alliance with the US, yes, but no more unconditional obedience.

The slogan "hard-headed internationalism" will undoubtedly fade, but the vision of a global society has the makings of a very big idea indeed. If Brown has the courage to follow his train of thought to its logical destination, Monday's speech may yet become a set text for the study of international affairs.